Question

If the circumference of base of a hemisphere is 2$\pi$ then it volume is ................... cm${}^3$.

• A. $\frac{2\pi }{3}{r}^3$
• B. $\frac{2\pi }{3}$
• C. $\frac{8\pi }{3}$
• D. $\frac{\pi }{12}$

Answer 1

Answer: (B)

$\frac{2\pi }{3}$

Circumference of the base of the hemisphere $=2\pi$ (given)
But circumference of the base of hemisphere = $2\pi r$
$\therefore 2\pi r=2\pi \Rightarrow r=1$
Now, volume of hemisphere $=\frac{2}{3}\pi r^3=\frac{2}{3}\pi (1{)}^3=\frac{2}{3}\pi$